Branching Process Models of Cancer
Title | Branching Process Models of Cancer PDF eBook |
Author | Richard Durrett |
Publisher | Springer |
Pages | 73 |
Release | 2015-06-20 |
Genre | Mathematics |
ISBN | 3319160656 |
This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As a consequence, the author calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the author evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis. These notes should be accessible to students who are familiar with Poisson processes and continuous time Markov chains. Richard Durrett is a mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles, and has supervised more than 40 Ph.D students. Most of his current research concerns the applications of probability to biology: ecology, genetics and most recently cancer.
Branching Process Models for Cancer Evolution
Title | Branching Process Models for Cancer Evolution PDF eBook |
Author | Ruibo Zhang |
Publisher | |
Pages | 0 |
Release | 2022 |
Genre | |
ISBN |
We study a multi-type branching process model associated with a transitional network between types. In particular, we are interested in determining the waiting time to each type in the network, employing an approximation of the process by its large time limit. We first present a literature review of results on large time limits and classify the dynamics of branching processes by their mean value matrices. For the special case when the transitional network is a single pathway, we present two approaches regarding approximating the waiting time for each type. To apply our theory to a real world problem, we use a multi-type branching process to model the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting time distributions of novel driver mutations.
Cancer Recurrence Times and Early Detection from Branching Process Models
Title | Cancer Recurrence Times and Early Detection from Branching Process Models PDF eBook |
Author | Stefano Avanzini |
Publisher | |
Pages | |
Release | 2019 |
Genre | |
ISBN |
Branching Processes in Biology
Title | Branching Processes in Biology PDF eBook |
Author | Marek Kimmel |
Publisher | Springer Science & Business Media |
Pages | 242 |
Release | 2006-05-26 |
Genre | Mathematics |
ISBN | 0387216391 |
This book introduces biological examples of Branching Processes from molecular and cellular biology as well as from the fields of human evolution and medicine and discusses them in the context of the relevant mathematics. It provides a useful introduction to how the modeling can be done and for what types of problems branching processes can be used.
Branching Processes
Title | Branching Processes PDF eBook |
Author | Patsy Haccou |
Publisher | Cambridge University Press |
Pages | 342 |
Release | 2005-05-19 |
Genre | Mathematics |
ISBN | 9780521832205 |
This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
Applications of Branching Processes to Cancer Evolution and Initiation
Title | Applications of Branching Processes to Cancer Evolution and Initiation PDF eBook |
Author | Michael David Nicholson |
Publisher | |
Pages | |
Release | 2018 |
Genre | |
ISBN |
The Physics of Cancer
Title | The Physics of Cancer PDF eBook |
Author | Caterina A. M. La Porta |
Publisher | Cambridge University Press |
Pages | 187 |
Release | 2017-04-20 |
Genre | Science |
ISBN | 1108150330 |
Recent years have witnessed an increasing number of theoretical and experimental contributions to cancer research from different fields of physics, from biomechanics and soft-condensed matter physics to the statistical mechanics of complex systems. Reviewing these contributions and providing a sophisticated overview of the topic, this is the first book devoted to the emerging interdisciplinary field of cancer physics. Systematically integrating approaches from physics and biology, it includes topics such as cancer initiation and progression, metastasis, angiogenesis, cancer stem cells, tumor immunology, cancer cell mechanics and migration. Biological hallmarks of cancer are presented in an intuitive yet comprehensive way, providing graduate-level students and researchers in physics with a thorough introduction to this important subject. The impact of the physical mechanisms of cancer are explained through analytical and computational models, making this an essential reference for cancer biologists interested in cutting-edge quantitative tools and approaches coming from physics.